Question

Rank the gases \(\mathrm{Xe}, \mathrm{CH}_{4}, \mathrm{~F}_{2},\) and \(\mathrm{CH}_{2} \mathrm{~F}_{2}\) in order of (a) increasing speed of effusion through a pinhole. (b) increasing time of effusion.

Short answer

Question: Rank the following gases in order of increasing speed of effusion through a pinhole and increasing time of effusion: Xe, CH4, F2, CH2F2. Answer: The order of increasing speed of effusion is CH4 < F2 < Xe < CH2F2, and the order of increasing time of effusion is CH2F2 > Xe > F2 > CH4.

Step-by-step solution

Understand Effusion

Effusion is the process by which a gas escapes through a small pinhole or orifice into an evacuated space. The speed of effusion depends on the molecular weights of the gases. Graham's law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molecular weight. Mathematically, this is represented as: \(r_1/r_2 = \sqrt{M_2/M_1}\) Where r_1 and r_2 are the rates of effusion for gas 1 and gas 2, and M_1 and M_2 are their molecular weights.

Calculate Molecular Weights

We first need to calculate the molecular weights of each gas. We can use the periodic table to find the atomic weights of the elements: Xe: Atomic weight = 131 g/mol CH4: C = 12 g/mol, H = 1 g/mol => Molecular weight = 12 + (4 x 1) = 16 g/mol F2: Atomic weight = 19 g/mol => Molecular weight = 2 x 19 = 38 g/mol CH2F2: C = 12 g/mol, H = 1 g/mol, F = 19 g/mol => Molecular weight = 12 + (2 x 1) + (2 x 19) = 52 g/mol

Rank Gases by Speed of Effusion

According to Graham's law of effusion, gases with lower molecular weights exhibit faster rates of effusion. Therefore, we can rank the gases based on their molecular weights in increasing order: CH4 (16 g/mol) < F2 (38 g/mol) < Xe (131 g/mol) < CH2F2 (52 g/mol) Thus, the order of increasing speed of effusion through a pinhole is: CH4 < F2 < Xe < CH2F2

Rank Gases by Time of Effusion

The time of effusion is inversely related to the speed of effusion. That is, a gas with a higher speed of effusion will take less time to effuse, and vice versa. Since we have already ranked the gases by their speed of effusion, we can simply reverse the order to rank them by increasing time of effusion: CH2F2 > Xe > F2 > CH4 Thus, the order of increasing time of effusion is: CH2F2 > Xe > F2 > CH4